Throughout this specification, including in the claims, the expression "power spectrum" is used in a broad sense to denote the result of any time-domain to frequency-domain transformation of a signal, including digital or analog signals representing frequency-amplitude spectra.
A large class of measured signals include narrow-band signal components (i.e., periodic, or nearly periodic, components) embedded in broad-band noise. Each narrow-band signal component may represent a narrow-band process of interest, such as a vibration mode of an object which radiates or reflects radiation.
Measured signals of this type are often transformed to generate their power spectra before they undergo subsequent processing. When the power spectrum of such a signal is displayed, the narrow-band components appear as peaks (each occupying a narrow frequency window). When several of the power spectra are displayed side-by-side (each spectrum representing a signal measured at different time), the narrow-band components representing a common process will align with each other so as to appear as a linear feature (a "narrow-band feature" or "track"). However, until the present invention it had not been known how practically to implement an accurate and automated procedure for distinguishing such linear features from noise.
In a variety of applications, it is useful to process a set of input signals (each measured at a different time) to study the time dependence of each signal's narrow-band content (for example, by tracking the center frequency, bandwidth, and amplitude of at least one narrow-band feature of each signal). Such signal processing operations are sometimes referred to as "frequency tracking" operations.
Examples of frequency tracking operations include surveillance operations in which positions of one or more moving radiation sources are monitored, and vibration analysis operations in which one or more operational states of a vibrating object under test are monitored.
For example, during sonar surveillance, a sequence of sonar signals may be gathered using an array of passive sonar sensors. Each sonar signal may include periodic components resulting from power generation and/or propulsion systems of one or more ocean-going vessels, embedded in strong background noise. When the power spectrum of one such sonar signal is displayed, it will include narrow peaks, some representing narrow frequency-band processes of interest, and some representing noise. If the peaks of interest can be distinguished from the noise, the power spectra of the sonar signals can be studied to classify, and track the position and operational state of each vessel (for example by studying relationships among the center frequencies, bandwidths, and amplitudes, of the peaks of interest over time).
Conventional automated techniques for performing "frequency-tracking" operations have suffered from serious limitations and disadvantages. A principal reason for the shortcomings of the prior art is the difficulty of implementing automated identification of distinct narrow-band features in each signal to be processed, in the general case that the number of features in each signal (and the character of noise in each signal) is unknown and time-varying. As a result, conventional narrow-band feature identification is often performed manually, by operators who manually mark features of interest on a special display.
One conventional approach to automated identification of narrow-band features has been to process the input signals in the time domain, by adaptively updating parameters representing the signals' narrow-band components. However, because this conventional approach assumes that a fixed, known, number of narrow-band components are present in each signal, the approach is unsuitable when the number of such components in each signal is unknown and variable from signal to signal.
Another class of conventional methods for automated identification of narrow-band features has been to process the input signals in the frequency domain. However, these methods either perform poorly (for example, ADEC and related methods such as those described in Mcintyre, et al., "A Comparison of Five Algorithms for Tracking Frequency and Frequency Rate of Change," Proc. ICASSP90, Albuquerque NM, April 1990, which are subject to spurious detections and other artifacts), or computationally very time-consuming and costly (for example, the MAPLE method described in Wolcin, "Estimation of Narrow-band Signal Parameters," J. Acoust. Soc. Am., Vol. 68, No. 1, July 1980).
The conventional ADEC method (to be described with reference to FIG. 1) identifies narrow-band features ("tracks") common to a set of input power spectra ("raw" power spectra) in the following way. Each raw power spectrum is searched over an "association gate" about a predicted track center frequency to select a peak (within the association gate) associated with a previously identified track. The selected peak is then processed to extract narrow-band process parameters therefrom (the "parameter estimation" operation represented in FIG. 1), and smoothing operations are then performed on the extracted process parameters (which can include center frequency, bandwidth, and amplitude) using corresponding parameters previously extracted from previously processed raw power spectra. An updated predicted center frequency, resulting from the smoothing operations, is employed to select subsequent associated peaks.
However, the present inventors have recognized that serious errors result from tight coupling (as in the ADEC method) of the steps of estimating "instantaneous" narrow-band process parameters (of a single raw spectrum) and smoothing the same parameters. For example, relatively large bandwidth processes can support many ADEC tracks, and processes with quickly changing center frequency can be represented by multiple, short-duration ADEC tracks.